Originally published in: Geophysical Research Letters, 23, 105-108,
1996
July 24, 1995; revised: October 16, 1995;
November 7, 1995

Abstract

Observations of the solar wind and the interplanetary
magnetic field from ISEE-3 are used as input to the gasdynamic
convected field model, as implemented in a new space weather forecast model.
Then the model output, for three case studies, is compared with
the magnetosheath quantities observed at
ISEE-2 in order to identify the sources of the observed variations of the
magnetosheath. It is found that some variations in the
magnetosheath plasma and magnetic field are well correlated with
corresponding variations in the solar wind
and hence have their sources in the solar wind. However, some variations in the
magnetosheath magnetic field correlate well with those in the solar wind
but not variations in plasma density. Finally, we find that
other variations in both plasma and magnetic field in the magnetosheath do
not have appreciable correlations with variations in the solar wind.
Most of these latter variations occur in the inner magnetosheath,
indicating that they are endogenous in origin. Our results show that the
forecast model can provide an accurate estimate of the timeshift from the
solar wind monitor to the magnetosheath, of the instantaneous locations of
the bow shock and magnetopause, and of the properties of the plasma
and magnetic field in the outer and middle magnetosheath.

Introduction

Changes in the solar wind plasma and the interplanetary magnetic field (IMF)
influence the processes in the magnetosphere, and are important sources of
many dynamic features observed at
the magnetopause and in the magnetosphere ( Elphic and Southwood, 1987;
Kivelson and Southwood, 1991; Song et al., 1992;
Russell et al., 1992; Le et al., 1993).

However, it is the nature of
the plasma and magnetic field of the magnetosheath
downstream of the bow shock that directly influences the magnetopause.
Since the upstream variations in the solar wind plasma can be significantly
modified upon
traversing the bow shock and magnetosheath (Yan and Lee, 1994),
the magnetosheath is an important region that any realistic
space weather forecast model cannot ignore.

Several theoretical models have been developed to understand the plasma
and magnetic field properties in the transition region from the bow shock
to the magnetopause. These models differ in the role that magnetic forces
play in them. (Spreiter et al., 1966) proposed a
gasdynamic model in which ordinary sound waves determine the properties of
plasma flow and field draping around the magnetopause and magnetic forces
play no role. Lees (1964) and Zwan and Wolf (1976) invoked
slow mode processes inherent to magnetized fluids and
found a depletion effect of the magnetosheath plasma.
Wu (1992) investigated the formation of a depletion layer close to the
magnetopause with a 3-D MHD calculation.

Song et al. (1990, 1992) studied processes
in the magnetosheath using data from ISEE-1 and 2 and discovered
a region of plasma density enhancements and field depression
near the magnetopause having a relatively large
spatial scale. They also inferred that in some cases this
slow-mode structure was locally generated in the magnetosheath
as part of the interaction of the magnetosheath with the magnetosphere
and was not one carried into the magnetosheath by the solar wind.
Moreover the plasma depletion
layer just outside the magnetopause often appears to be associated
with a decline in density beginning at
the slow-mode structure. Hammond et al. (1995) have recently
reported a similar structure in the Jovian magnetosheath.
Using a two-dimensional MHD simulation,
Lee et al. (1991) showed that such a structure can be formed
close to the stagnation region. Southwood and Kivelson (1992) suggested
that slow-mode structures or slow wave fronts can be formed
by sources of disturbances at the magnetopause.
The structure may play an important role in establishing
the flow and field pattern near the magnetopause (Song et al.,
1992).

Omidi and Winske (1995)
pointed out that the slow-mode wave front
may originate at the magnetopause and that upstream mirror mode waves
may play some roles. On the other hand,Yan and Lee (1994)
drew attention to the possibility that slow-mode structures
can be formed through the interaction
between interplanetary rotational discontinuities and the
bow shock, and hence some slow-mode
magnetosheath variations may have their sources in the solar wind.
Therefore, in order to understand the properties of the slow-mode
structure and other processes in the magnetosheath, it is important
to identify the sources of the
variations observed in the magnetosheath. This work
will examine in addition the validity and limitations of the gasdynamic convected field model.

Approach

In principle, a direct approach to study large scale
structures in the magnetosheath would be to solve the three-dimensional magnetohydrodynamic (3-D MHD) equations
in a realistic magnetosheath geometry. However, at present,
there is no convenient time-dependent global 3-D MHD model
available for routine use in comparative studies of
magnetosheath observations. In this paper we use
the gasdynamic convected field
model (GDCFM) (Spreiter et al., 1966;
1968; Spreiter and Stahara, 1980) recently implemented in
a space weather forecasting model (Stahara and Spreiter, manuscript
in preparation) to study the correlation of variations in the magnetosheath
with those in the solar wind. In this model the gasdynamic flow
solution is calculated ignoring magnetic forces. Then the magnetic field
lines are computed by convecting them through the fluid like dye lines or
threads exerting no force on fluid. We have found that the gasdynamic
forecast model can provide three
important baselines for magnetosheath studies. First,
the model can provide a relatively accurate timeshift
between the solar wind monitor and the magnetosheath observer.
Second, the model provides reference estimates of magnetosheath
properties including the density, bulk velocity, temperature and magnetic
field throughout the magnetosheath. Third, the model provides the expected locations of the bow shock and the magnetopause. Although the predictions are
only an approximation to the fully time-dependent 3-D MHD solution, the
physics included in the model is well understood, and exogenous variations
are predicted systematically. Therefore, we use the model prediction
as a baseline to study the frequently observed variations in the magnetosheath.
We use the solar wind plasma and IMF measurements
to drive the forecast model and select the point for the prediction
according to the location of the satellite in the magnetosheath.
Comparison of the results from the GDCFM (which approximates the fast but not
Alf-ven and slow mode processes) with magnetosheath
observations can separate the effects of solar wind variations
from the magnetosheath Alf-ven and slow mode processes, and
serve to identify
the sources of large scale variations involving these structures in the
magnetosheath.

The magnetosheath data are from the ISEE-2 magnetometer
(Russell 1978) and Fast Plasma
Experiment (FPE) (Bame et al., 1978a). The solar wind data
are obtained by the
magnetometer (Frandsen et al., 1978) and solar wind analyzer
(Bame et al., 1978b) on ISEE-3. In this letter, we present
three crossings in detail. The first case involved
strong variations in both the solar wind plasma density and IMF.
The second involved significant changes only
in the IMF, but not in the solar wind plasma properties.
The third occurred during relatively steady
solar wind and IMF conditions.

Results

Case 1.Figure 1 shows an outbound crossing
of the magnetosheath by ISEE-2 on September 12,
1978. Solid lines are plasma and magnetic field properties in GSE
coordinates from ISEE-2 with 12 sec. solution and dashed lines
are the forecast model predictions with a time solution of 1 min.
ISEE-2 was located at (8.7, -1.9, 3.9)R
GSE at 2000 UT and (13.3, -0.1, 5.4)R
GSE at 2400 UT. ISEE-3 was upstream of the bow shock
in the solar wind near (207, -68, 18)R
GSE during this period.
The timeshift between ISEE-3 and ISEE-2 is about 50 min.

Figure 1.
An outbound magnetosheath crossing by ISEE-2 (solid lines)
and corresponding GDCFM prediction (dashed lines). The positions of
the magnetopause and the bow shock are indicated by arrows. The solar wind
Mach number M=6.0, Alfven Mach number
M=7.5 and =1.44

Several strong plasma density enhancements with large time scales
are observed in the magnetosheath. The enhancement between
2145 and 2217 UT is well predicted by the model. Furthermore, the model
predicts that ISEE-2 is very close to the bow shock during this time
as evidenced by a pair of predicted but not observed bow shock crossings.
The density prediction in general is good near the bow shock but
higher than observed near the magnetopause. The difference
is as large as 60o . There is a prediction of multiple
magnetopause crossings, which are not actually recorded by
ISEE-2. The actual slowdown of the magnetosheath
flow as evidenced in the V
component is significantly less
than the prediction. Since the FPE was not
designed to measure the solar wind and has widely separated energy channels
[Bame et al., 1978a], its velocity in the solar wind is
different in magnitude from that of ISEE-3. The V
component of
the observed velocity is positive from 2145 UT to the bow shock while
the y component of ISEE-2 position is negative. The difference in sign is
due to the aberration effect that is properly included in the forecast model.
Prediction of the three components and magnitude of magnetic field is in
good agreement with the observation except for some small regions
principally from the magnetopause to 2145 UT.
Because the model is a single fluid model, the temperature is considered
to be the sum of
the proton and electron temperatures.
The predicted temperature is about 50% lower than the observation,
and the difference becomes somewhat greater corresponding to the slow mode structures.

Case 2.
An outbound crossing of the magnetosheath on September 17, 1978
by ISEE-2 is shown in Figure 2
(in the same format as in Figure 1).
This case has been previously studied by Song et al. [1992]. ISEE-2 was
at (9.0, -2.4, 4.1)R GSE at 1500 UT and (12.5, -1.4, 5.2)
R
GSE at 1800UT. ISEE-3 was located at (211, -80, 17)R
GSE.
The timeshift between ISEE-3 and ISEE-2 observations is approximately
57 min. The solar wind was relatively steady, while the IMF rotated
about 130o near 1510-1540UT and about 54o near 1550-1610UT.

Figure 2.
An outbound
magnetosheath crossing
in the same format as Figure 1. The solar wind
Mach number M=5.0, Alfven Mach number
M=9.0 and
3.2

The magnetic field prediction agrees very well with the observations
throughout the magnetosheath except for a thin region near the magnetopause. ISEE-2 detected plasma density enhancements from 1533 UT
to 1610 UT with the peaks more than double the background value.
The model predictions of density during this time show no
indication of this structure. Again, the
magnitude of V
is significantly larger than the perdiction.
The V is reasonably well predicted, but the observation
shows a significant additional deflection within the large-scale slow mode structure.
There is little fluctuation in observed and
predicted temperatures, but the prediction again is approximately
50% lower than the observation. Within the large-scale slow mode structure,
the correlation with the solar wind is good for the direction of
the magnetic field
but the predicted plasma density shows little correlation with the observed
density variations.

Case 3.Figure 3 presents an inbound magnetosheath pass
on September 5, 1978 by ISEE-2 (in
the same format to Figure 1). ISEE-2 was at (8.6, 10.0, 2.0
)RGSE at
0200 UT and (7.6, 9.5,1.7) R
GSE at 0500UT. ISEE-3 was located at
(195.6, -48.2, 18.3)R GSE. The timeshift fom ISEE-3 to
ISEE-2 is about 51 min. A major difference between
this case and previous two is that this pass occurred at a much
greater solar zenith angle, about 50o from the stagnation
streamline.

Figure 3.
An inbound magnetosheath crossing in a format similar to Figure 1,
but with plasma the ratio of the thermal pressure
to the magnetic pressure shown in the bottom panel. The solar wind
Mach number M=5.5, Alfven Mach number
M=9.0 and =3.0

Again, the model predictions for this pass are in good agreement with
the observations in the magnetosheath except for a small region
near the magnetopause.
The changes of the plasma density and the magnetic field predicted by
the model are
very small for this pass because of the steady upstream condition.
The slow mode structure with a plasma density enhancement and field
decrease occurs from 0410 UT to 0440 UT and is not predicted by the model.
The predictions of velocity components are much better than the other
two cases and the aberration
effect may become unimportant because the satellite was far from the
stagnation streamline (nearly 10R). The plasma
is
a good indicator of slow mode processes because the thermal and magnetic
pressures change out of phase. The predicted and observed s are about
the same in the magnetosheath other than within the slow mode structure.
There is no correlation
between plasma density and magnetic field variations in the slow mode
structure with those in the solar wind (after having examined the
corresponding conditions in the solar wind).

Summary and Discussion

In the three cases we have shown, the large time scale
variations of the plasma density and
magnetic field in the magnetosheath have different sources.
Case 1 shows that some variations in the magnetosheath are driven
by sources in the solar wind as evidenced by the good correlation
of the variations of density and magnetic field between
the solar wind and the magnetosheath.
Such variations in the solar wind can penetrate the bow shock
into the magnetosheath and may be modified in the nonuniform
magnetosheath medium [Yan and Lee, 1994].
Case 2 shows that there is good correlation
of the magnetic field in the solar wind and in the magnetosheath, but
corresponding plasma density enhancements in the inner magnetosheath do
not necessarily have a solar wind origin. Although large-scale slow-mode
variations may be generated by variations in the IMF direction
without plasma density variations through wave-wave
interactions at the bow shock,
the structure for this case does not seem to be generated this way
because of the smallness of the field rotation (less than 54o)
associated with the outer front of the slow-mode structure.
For case 3, there seems to be no appreciable correlation in the plasma
density
or magnetic field between the solar wind and the inner magnetosheath
variations from the observed structure although they are well-correlated in
the outer and middle magnetosheath. This case shows the
slow-mode structures to be locally
generated in the magnetosheath rather than carried by the solar wind
and their occurrence is independent of the variations of the IMF direction.
This result confirms the interpretation by Song et al. [1992].

For all these cases studied, there is an overestimate of the density
prediction near the magnetopause.
In some cases, the difference can be as
large as 60%. Of the 60%, less than 10% may be accounted for by
the compression included in the GDCFM. The remaining more than 50\% is most likely due to
the plasma depletion effect. We note that the depletion effect appears to
occur over the entire magnetosheath and not only in the small region near the
magnetopause.
We will further investigate this phenomenon
statistically. Another interesting phenomenon is that the flow often
slows down much less in the magnetosheath than predicted.

Determination of the timeshift has been a crucial issue when
correlating the variations in the solar wind with those in the magnetosheath,
and then with subsequent variations on the magnetopause,
in the magnetosphere and
ionosphere and on the ground. In the past several methods have been used:
(1) dividing the distance in the x direction between the two spacecraft
by the measured solar wind velocity;
(2) determining the propagation delay when the solar wind monitor is not on the Sun-Earth line, assuming that the surface of constant IMF and
solar wind contain both ecliptic pole and the path spiral direction;
(3) similar to (2) but determining the normal to the surface of constant solar wind conditions by some technique such as minimum variance at the upstream monitor; and (4) shifting the time in order to maximize the correlation between
the clock angle of the IMF and that of the sheath field
[Song et al., 1992]. There are large uncertainties in the time
delay using each of methods (1),(2)
and (3). While method (4) is significantly better, only one timeshift is provided and it cannot account for the changes in the time shift when
the solar wind velocity changes. Our method is similar to method (1)
but with the advantage that the variation of velocity along the streamline with magnetosheath is properly accounted for prediction.

From the three presented cases, we have found that the thickness of
magnetosheath is well predicted by the model,
i.e., one may change
either the magnetopause or
the bow shock crossing time to improve its timing prediction, but it will
worsen the other. Furthermore, the time shifts we used determine well
the time of those field changes in the sheath whose origin was
in the wind. Practically, one has no freedom in shifting the time.
The bulk velocity, magnetic field and plasma density are in general
well predicted by the model in the outer and middle magnetosheath
while the predictions may become significantly different from
the observations in the region near the magnetopause. As a whole,
we find that the forecast model can provide a relatively accurate
time shift with an
uncertainty of less than 10 min., provide good reference locations of
the bow shock and the magnetopause, and predict the magnitudes of the
parameters reasonably well in the outer and middle magnetosheath.
This justifies the use of the model predictions as a baseline to correlate the variations in the magnetosheath with those in the solar wind.
The differences near the magnetopause and within the slow mode structure
are due to the MHD effects not included in the model.

Acknowledgments

XXZ would like to thank the HAO/NCAR
for support as a visiting scientist, and was sponsored by the Chinese
Academy of Sciences and the NSF of China under
grant 49404054.
Work at HAO was sponsored by the NSF and supported
by NASA under research grant W-18,582. Work at RMA was supported by
the NSF under research grant ATM-9301022.
Work at UCLA was supported by NASA under research grant NAGW-3948.
We thank J. T. Gosling for providing us ISEE-2 data and NSSDC for
ISEE-3 data.